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Math Help - Complex Contour Integration of Real Improper Integrals

  1. #1
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    Complex Contour Integration of Real Improper Integrals

    Does any body know how to go about doing the following Integrals using complex contour integration (upper half semicircle contour):

    1) Integrate from 0 to infinity 1/(2+x+x^3) dx




    2) Integrate from 1 to infinity 1/(x*sqrt(x^2-1)) dx
    Last edited by heatly; May 20th 2014 at 10:14 PM.
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  2. #2
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    Re: Complex Contour Integration of Real Improper Integrals

    Integrals of Rational Functions

    has everything you need to know.

    you can search for "How to evaluate an improper integral with a contour integral." to skip directly to it.
    Thanks from heatly and LimpSpider
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    Re: Complex Contour Integration of Real Improper Integrals

    Thanks,much appreciated.
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    Re: Complex Contour Integration of Real Improper Integrals

    I had a look at that site....very helpful,but the integral I posted: Integral 0 to infinity 1/(2+x+x^3) is an odd integrand,so cant use a semicircle contour.I couldn't find anything on that site when dealing with an odd integrand

    What contour should I use for this problem? I have tried using a sector but couldn't get it to work...
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